if 1/1^2 + 1/3^2 + 1/5^2 + ............. =x^2/8 then find 1/1^2 + 1/2^2 +1/3^2 + 1/4^2+............

Question

Accepted Answer

L e t space 1 over 1 squared plus 1 over 2 squared plus 1 over 3 squared plus 1 over 4 squared plus............ space equals space K rightwards double arrow open parentheses 1 over 1 squared plus 1 over 3 squared plus 1 over 5 squared plus...... close parentheses plus open parentheses 1 over 2 squared plus 1 over 4 squared plus 1 over 6 squared plus.... close parentheses equals K space left parenthesis s e p a r a t i n g space o d d space a n d space e v e n space t e r m s right parenthesis rightwards double arrow open parentheses x squared over 8 close parentheses plus open parentheses 1 over 2 squared open parentheses 1 over 1 squared plus 1 over 2 squared plus 1 over 3 squared plus..... close parentheses close parentheses equals K rightwards double arrow open parentheses x squared over 8 close parentheses plus open parentheses 1 over 2 squared open parentheses K close parentheses close parentheses equals K rightwards double arrow K open parentheses 1 minus 1 fourth close parentheses equals x squared over 8 rightwards double arrow fraction numerator 3 K over denominator 4 end fraction equals x squared over 8 rightwards double arrow K equals 4 over 3 cross times x squared over 8 equals x squared over 6 rightwards double arrow 1 over 1 squared plus 1 over 2 squared plus 1 over 3 squared plus 1 over 4 squared plus............ space equals x squared over 6

Related Videos